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Towards a unified setting for non-monotony and paraconsistency

Grant number: 13/22371-0
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2014
Effective date (End): September 30, 2016
Field of knowledge:Humanities - Philosophy - Logic
Principal Investigator:Walter Alexandre Carnielli
Grantee:Gabriele Pulcini
Home Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:10/51038-0 - Logical consequence, reasoning and computation - LOGCONS, AP.TEM


The research programme here proposed concerns the philosophy of logic, especially the long-standing debate about logical monism and pluralism. Monists like Quine uphold the idea that the only right logic is classical logic, other deviant calculi - intuitionistic, paraconsis- tent and, in general, non-classical systems [26, 18, 29] - being essentially based on misconceptions of the very role and meaning of logical connectives [21]. On the opposing side, relativists argue against such alleged uniqueness by supporting a pluralism in which divergent non-classical calculi fit in with different semantical contexts in this way receiving their own epistemological justification [1]. From the applicative point of view, logical pluralism is supported by many well-known research fields like artificial intelligence, cognitive science and recent developments in computer science. Nonetheless, such a pluralistic attitude involves many philosophical problems like those related to the notion of logical consequence and the nature of connectives, which still need further explanation [7, 2].We propose to design a unitary framework able to uniformly encompass classical logic as well as a considerable portion of non-classical logics, especially those dealing with non-monotony and paraconsistency, and in this way reassess and possibly provide a definitive answer for some of the philosophical puzzles involved in logical pluralism [7, 1, 12]. Such a uniform framework is expected to be obtained by means of the control sets logical device, a metalogical apparatus introduced and partially discussed in [6, 9]. The intuitive idea is that a control set gathers all the logical contexts which are supposed to block a certain derivation. Carrying out this task, both syntactical and semantical issues are involved, especially in relation to substructural logics [19] and Logics of Formal Inconsistency [8]. (AU)

Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
PIAZZA, MARIO; PULCINI, GABRIELE. Unifying logics via context-sensitiveness. JOURNAL OF LOGIC AND COMPUTATION, v. 27, n. 1, p. 21-40, FEB 2017. Web of Science Citations: 6.
PIAZZA, MARIO; PULCINI, GABRIELE. Uniqueness of axiomatic extensions of cut-free classical propositional logic. LOGIC JOURNAL OF THE IGPL, v. 24, n. 5, p. 708-718, OCT 2016. Web of Science Citations: 0.
BONIOLO, GIOVANNI; D'AGOSTINO, MARCELLO; PIAZZA, MARIO; PULCINI, GABRIELE. Adding logic to the toolbox of molecular biology. EUROPEAN JOURNAL FOR PHILOSOPHY OF SCIENCE, v. 5, n. 3, p. 399-417, OCT 2015. Web of Science Citations: 6.
D'AGOSTINO, MARCELLO; PIAZZA, MARIO; PULCINI, GABRIELE. A logical calculus for controlled monotonicity. JOURNAL OF APPLIED LOGIC, v. 12, n. 4, p. 558-569, DEC 2014. Web of Science Citations: 4.

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